Method and device for training manipulation skills of a robot system

ABSTRACT

A method of training a robot system for manipulation of objects, the robot system being able to perform a set of skills, wherein each skill is learned as a skill model, the method comprising: receiving physical input from a human trainer, regarding the skill to be learned by the robot; determining for the skill model a set of task parameters including determining for each task parameter of the set of task parameters if a task parameter is an attached task parameter, which is related to an object being part of said kinesthetic demonstration or if a task parameter is a free task parameter, which is not related to a physical object; obtaining data for each task parameter of the set of task parameters from the set of kinesthetic demonstrations, and training the skill model with the set of task parameters and the data obtained for each task parameter.

CROSS REFERENCE

The present application claims the benefit under 35 U.S.C. § 119 of German Patent Application No. DE 102019216560.5 filed on Oct. 28, 2019, which is expressly incorporated herein by reference in its entirety.

FIELD

The present invention relates to a method and device for training a robot system.

BACKGROUND INFORMATION

Robot systems are used for manipulation of objects

Robot manipulation skills such as picking, inserting, and dropping are often hard-coded for a particular task. This however results in poor flexibility and re-usability in case of new scenarios such as different workspaces or varying conditions.

Further, it is conventional to train a robot system with demonstration. Simply recording and replaying a demonstrated trajectory is often insufficient, because changes in the environment, such as varying robot and/or object poses, would render any attempt unsuccessful.

SUMMARY

The present invention provides a method and system with which the learning of new skills and tasks can be implemented in an efficient and easy way.

This may be achieved by example devices and methods according to the present invention.

In accordance with an example embodiment of the present invention, a method of training a robot system, in particular for manipulation of objects, the robot being able to perform a set of skills, wherein each skill is learned as a skill model in particular as a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model, comprises the steps of:

receiving physical input, in particular from a human trainer, regarding the skill to be learned by the robot, wherein the physical input comprises a set of kinesthetic demonstrations on the robot system; determining for said skill model a set of task parameters, wherein the step of determining the set of task parameters comprises determining for each task parameter of said set of task parameters if a task parameter is an attached task parameter, which is related to an object being part of said kinesthetic demonstration or if a task parameter is a free task parameter, which is not related to a physical object; obtaining data for each task parameter of said set of task parameters from the set of kinesthetic demonstrations, and training said skill model with said set of task parameters and said data obtained for each task parameter.

Preferably, a skill is learned as a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model.

A basic feature of learning from demonstration is to fit a prescribed skill model such as GMMs, Gaussian Mixture Models; to a handful of demonstrations. For each skill, the trainer, in particular a human trainer performs several, in particular a number of M_(a) kinesthetic demonstrations on the robot. Each demonstration contains T_(m) data points for a dataset of N=Σ_(m=1) ^(M) T_(m) total observations ξ={ξ_(t)}_(t=1) ^(N) where ξ_(t)∈

^(d). Preferably, the demonstrations are recorded from the perspective of P different coordinate systems TP, which are also referred to as the task parameters. For obtaining data for the task parameters the demonstrations are transformed from global frame to frame p∈TP,

ξ_(t) ^((p)) =T _((b) _(t) _((p)) _(,A) _(t) _((p)) ₎ ⁻¹(ξ_(t))=A _(t) ^((p)) ⁻¹ (ξ_(t) −b _(t) ^((p))),

where (b_(t) ^((p)), A_(t) ^((p))) is the translation and rotation of frame p with regard to a reference frame, in particular the world frame at time t.

A TP-GMM is described by the parameters

{π_(k),{μ_(k) ^((p)),Σ_(k) ^((p)) }p∈TP} _(k=1) ^(K)

where K represents the number of Gaussian components in the mixture model, π_(k) is the prior probability of each component, and μ_(k) ^((p)), Σ_(k) ^((p)) are mean and covariance of the k-th component within frame p.

Once learned, the TP-GMM can be used during execution to reproduce a trajectory for the learned skill. Namely, given the observed frame {(b_(t) ^((p)), A_(t) ^((p))}_(p∈TP), the learned TP-GMM is converted into one single GMM with parameters {π_(k), {μ_(t,k) ^((p)), Σ_(t,k) ^((p))}p∈TP}_(k=1) ^(K), by multiplying the affine-transformed Gaussian components across different frames, as follows

${\left( \Sigma_{t,k} \right)^{- 1} = {\sum\limits_{p \in {TP}}\left( \Sigma_{t,k}^{(p)} \right)^{- 1}}},{\mu_{t,k}^{(p)} = {\Sigma_{t,k}{\sum\limits_{p \in {TP}}{\left( \Sigma_{t,k}^{(p)} \right)^{- 1}\mu_{t,k}^{(p)}}}}},$

where parameters of the updated Gaussian at each frame p are computed μ_(t,k) ^((p))=A_(t) ^((p))μ_(k) ^((p))+b_(t) ^((p)) and Σ_(t,k) ^((p))=A_(t) ^((p))Σ_(k) ^((p))A_(t) ^((p)) ^(T) . For more details, reference is made to CALINON Sylvain: “A tutorial on task-parameterized movement learning and retrieval.” Intelligent Service Robotics, 9(1):1-29, 2016.

Hidden semi-Markov Models (HSMMs) extend standard hidden Markov Models (HMMs) by embedding temporal information of the underlying stochastic process. That is, while in HMM the underlying hidden process is assumed to be Markov, i.e., the probability of transitioning to the next state depends only on the current state, in HSMM the state process is assumed semi-Markov. This means that a transition to the next state depends on the current state as well as on the elapsed time since the state was entered.

Exemplary details of applying Hidden semi-Markov Models in combination with Task-Parameterized Gaussian Mixture Models (TP-GMMs), for robot skill encoding to learn spatio-temporal features of the demonstrations are described, for example, in the following reference: TANWANI, Ajay Kumar, CALINON Sylvain: “Learning Robot Manipulation Tasks with Task-Parameterized Hidden Semi-Markov Model.” IEEE Robotics and Automation Letters, pages 1-8, 2016.

More specifically, a task-parametrized HSMM model consists of the following parameters

θ = {{a_(kh)}_(h = 1)^(K), (μ_(k)^(D), σ_(k)^(D)), {π_(k), {μ_(k)^((p)), Σ_(k)^((p))}_(p ∈ TP)}}_(k = 1)^(K)

where α_(kh) is the transition probality from state k to h; (μ_(k) ^(D), σ_(k) ^(D)) describe the Gaussian distributions for the duration of the state k, i.e., the probability of staying in state k for a certain number of consecutive steps; and

{π_(k), {μ_(k)^((p)), Σ_(k)^((p))}_(p ∈ TP)}_(k = 1)^(K)

is the TP-GMM as described above and for each k, describe the emission probability, i.e., probability of observation, corresponding to state k. The prior π_(k), however, describes in an HSMM only the probability distribution of the initial component at t=1. The probability distribution of the components at subsequent time steps is determined via the underlying Semi-Markov Model. Note that in an HSMM each state corresponds to a Gaussian component in the associated TP-GMM.

Preferably, the structure of the Semi-Markov Model is linear, which means the sequence of states is deterministic and only the duration in each state is probabilistic. This linear structure can be achieved by setting π_(k)=δ_(1k) and α_(kh)=δ_((k+1)h) with δ_(ij)=0 for i≠j and δ_(ij)=1 for i=j. By assuming a linear structure, each skill follows the same segments and is trained in separate model. Preferably, no bifurcations are needed.

Preferably, the aforementioned TP-HSMM formalism is adapted to the Riemannian manifold, for a detailed theory of which reference is made to ZEESTRATEN, Martijn: “Programming by demonstration on Riemannian manifolds.” 2017. PhD thesis, Department of Informatics, Bioengineering, Robotics, System Engineering, DIBRIS University of Genova, and Department of Advanced Robotics Istituto Italiano di Tecnologia.

For each skill, the trainer, in particular a human trainer performs several kinesthetic demonstrations on the robot. Each kinesthetic demonstration comprises a sequence of states consisting of states of an end-effector of the robot system and consisting of states of the object being part of the kinesthetic demonstrations.

Particularly, for skill a∈A, wherein A is a set of manipulation skills, the set of objects involved is given by O_(a) ∈O and the set of demonstrations is given by D_(a)={D₁, . . . D_(Ma)}, where each demonstration is given by

D_(m) = [s_(t)]_(t = 1)^(Tm) = [(ξ_(t){p_(t, o), o ∈ O_(a)})]_(t = 1)^(Tm),

where D_(m) is a sequence of states s that consists of the robot end-effector state ξ within the manifold M_(ξ) and object states {p_(o), o∈O_(a)} each within the manifold M_(p). Via a combination of these skills, these objects can be manipulated to reach a desired final state.

According to the present invention, a skill enables the robot system to manipulate an object. In the following it is differentiated between core skills comprising a desired final state of the object and transition skills where the final state of the object can be freely chosen during demonstration.

The set of task parameters of the skill model is essential for the flexibility and generalization of the skill. By this, the characteristics of the demonstration can be learned from different perspectives. According to the present invention, two different types of task parameters are introduced.

On the one hand, task parameters are usually attached to the objects relevant to the skill and constructed from their poses. These are referred to as attached task parameters. An attached task parameter can be constructed from an object pose p∈M_(p). For instance, for M_(ξ)=M_(p)=

³×S³, the associated task parameter is given by b=p and A=diag(R, I₃) where R is the rotation matrix corresponding to the orientation in p.

On the other hand, for transition skills there are however further relevant task parameters that are not related to a physical object. These are referred to as free task parameters. A free task parameter can not be perceived and should be set explicitly by the user or a planning algorithm. The choice determining a parameter being a free task parameters directly influences the outcome of executing transition skills.

The example method according to the present invention enables advantageously to train the robot system with new skills in a general way, as the robot system is able to recognizes and encode the intention behind a demonstration.

Therefore, the success rate of a new skill is improved.

Further, the example method according to the present invention enables advantageously to learn new skills without implementing a simulation model.

According to an embodiment, the step of determining the set of task parameters comprises choosing the task parameters among the following: task parameters associated with a pose of the object being part of said kinesthetic demonstration, free task parameters, or task parameters associated with a pose, in particular an initial pose, of and end effector of the robot system. In particular, for a skill a, the set of task parameters, denoted by TP_(a) can be chosen among the following: the set of relevant objects O_(a), the set of free task parameters, denoted by F_(a), and the robot arm initial pose, denoted by r. Generally, the set of tasks parameters can be chosen by attaching frames to all involved objects O_(a) and to the robot arm initial pose indexed by r as well as using the free task parameters F_(a) for transition skills, i.e., TP_(a)=O_(a) ∪F_(a) ∪{r}.

Advantageously, by choosing an appropriate set of task parameters computation cost might be increased and/or performance of reproduction might be decreased.

According to an example embodiment, the step of choosing the task parameters is based on a validation of the reproduction error of said choice. For this we need a ground truth, which is given as demonstration. Usually, the set of demonstrations is rather small, such that the same set of demonstrations Da is used for training and validation. This yields to the validation:

${V\left( {TP}_{a} \right)} = {\sum\limits_{m = 1}^{M_{a}}\;{\overset{T}{\sum\limits_{t = 1}^{T_{m}}}\;{{\log_{\xi_{t}}\left( \xi_{t} \right)}}}}$

where ξ_(t) is the trajectory retrieved from a skill model for the task parameters TP_(a) from a demonstration, with M_(a) is the number of demonstrations wherein each demonstrations contains Tm data points for a dataset of for a dataset of N=Σ_(m=1) ^(M) T_(m) total observations.

In case that the number of involved objects for a skill is small, the model can be trained for all combinations of task parameters and each choice can be validated using the above described validation. If the number of objects is higher, the trainer might preferably preselect some promising choices of task parameters to reduce the computation time.

According to an example embodiment, the method further comprises the step of learning a precondition model of a skill, which refers to a relative relations between the robot system, in particular and end-effector of the robot system, and an object at an initial time. Preferably, the precondition is satisfied when executing a skill to ensure an successful execution. The learned skill model as described above contains information where the robot arm, in particular the end-effector, would start from, but does not incorporate information about the rest of an environment of the robot system, in particular the objects. Such information should include how the objects and the robot arm, in particular the end effector are located with regard to each other when the execution of a specific skill starts. Therefore, according to an example embodiment, a task parameterized Gaussian, TP-G, is learned for each object to fit its poses from the demonstrations. More specifically, the precondition model of a skill is defined by

${\gamma_{1,a}\left( {s,p_{F}} \right)}\overset{\Delta}{=}\left\{ {\left( {\mu_{1,o}^{(p)},\Sigma_{1,o}^{(p)}} \right),{\forall{p \in {{TP}_{a}\backslash\left\{ o \right\}}}}} \right\}_{o \in {O_{a}\bigcup F_{a}}}$

where (μ_(1,o) ^((p)), Σ_(1,o) ^((p))) is the Gaussian distribution of object o's initial pose at time 1 from perspective of object p's initial pose at initial time 1.

Advantageously, the precondition model can be learned purely from the kinesthetic demonstrations performed on the robot system.

According to an example embodiment of the present invention, the method further comprises the step of learning an effect model of skill, which refers to a relative relation between the robot system, in particular, and end-effector of the robot system and an object at a final time. The effect of a skill is the resulting system state after executing the skill, which includes both the poses of robot arm and involved objects. The learned skill model as described above contains information where the robot arm, in particular the end-effector, would stop at, but does not incorporate information about the rest of an environment of the robot system, in particular the objects. Such information should include how the objects and the robot arm, in particular the end effector are located with regard to each other when the execution of a specific skill finishes. Therefore, according to an embodiment a task parameterized Gaussian, TP-G, is learned for each object to fit its poses from the demonstrations. More specifically, the effect model of a skill is defined by

${\gamma_{T,a}\left( {s,p_{F}} \right)}\overset{\Delta}{=}\left\{ {\left( {\mu_{T,o}^{(p)},\Sigma_{T,o}^{(p)}} \right),{\forall{p \in {TP}_{a}}}} \right\}_{o \in O_{a}}$

where (μ_(T,o) ^((p)), Σ_(T,o) ^((p))) is the Gaussian distribution of object o's final pose at time T from the perspective of object p's initial pose at initial time 1.

Advantageously, the skill model can be learned purely from the kinesthetic demonstrations performed on the robot system.

In practice, different task parameters can be chosen for γ_(1,α) and γ_(T,α) to incorporate not only relative but also absolute conditions. Preferably, the skill model and/or the precondition model is computed within the object pose manifold

_(p).

According to a further embodiment of the present invention, the method comprises the steps of evaluating a measure of the precondition of a skill using the precondition model. In particular, the product of the observation probability for the robot system, in particular the robot arm, and each object, or equivalently the sum for their logarithmic values can be computed. The measure provides a continuous value that evaluates how similar a current situation is to the ones demonstrated during the kinesthetic demonstration. This measure can be already useful in the following ways: it can be compared with a given threshold to decided whether the precondition of skill a is satisfieded, or it can be used to compare different scenarios and different free task parameters in p_(F), and to decide which one satisfies the precondition more.

According to a further embodiment of the present invention, the method comprises further the step of predicting an effect of a skill using the effect model. This prediction can be useful to predict the effect of a skill which is the resulting system state after executing the skill, which includes both the poses of robot arm and involved objects.

The present invention also includes a robot system configured being trainable via physical input, in particular from a human trainer, regarding the skill to be learned by the robot, wherein the physical input comprises a set of kinesthetic demonstrations on the robot, according a method according to any of the described embodiments.

According to an example embodiment, the method further comprises optimizing the confidence of a skill sequence. A measure of confidence is used to measure how likely it is to perform the skill successfully within a new scenario and/or under new conditions.

According to an example embodiment of the present invention, the robot system is configured to track a reference trajectory with an end-effector of the robot system.

According to an example embodiment of the present invention, the robot system is configured to detect objects of interest.

The present invention also includes a computer for controlling a robot system according to the embodiments, wherein the computer is configured to execute the method according to the embodiments.

The present invention also includes a computer program comprising computer program code, the computer program code when being executed on a computer enabling said computer to perform the method according to the embodiments.

The present invention also includes a machine-readable storage medium comprising the computer program according the embodiments.

The present invention also includes the use of a robot system, in particular for manipulation of objects, the robot being able to perform a set of skills, according to the embodiments for executing a skill sequence comprising a set of skills learned by the robot system according to the method according to any of the embodiments and/or with a computer according to the embodiment and/or with a computer program according to the embodiment.

After determining the optimal choice of free task parameters according to the method described above, a skill sequence is executed as follows. Starting from h=0, the actual system state s_(h) including the poses of all relevant objects and the robot arm are obtained from the state estimation system such as perception and robot state estimator. Then the associated task parameters are constructed from s_(h) according to the optimal choice of task parameters used during the training of the skill model. If a skill is a transition skill, the free task parameters associated with the 1 objects can not be obtained from the state estimation system, instead should be set according to the optimal choice as described above. Thus, given the complete set of task parameters, the GMM components can be computed.

The above process is summarized in the following Algorithm 1. The training process between Line 2 to 5 is done offine for each skill a in the set of skills A. During execution, after observing the initial state s₀, the optimal task parameter p_(F) is computed in Lines 6 and 7. Then, each skill is executed as described in Lines 9 to 14, which makes use of the learned models and the optimization results.

Algorithm 1: Optimize Transition Skills for Manipulation Tasks

Input: Set of skills A; demonstration D_(a) for each a∈A; skill sequence a. 1 for each each a∈A //during training 2 Choose task parameters TPa. 3 Train TP-HSMM model θ_(a) in given TP_(a) and D_(a). 4 Learn the precondition distribution θ1,a in given TP_(1,a) and D_(a). 5 Learn the system state evolution θT,a in given TP_(T,a) and D_(a). 6 Observe the initial system state s₀. //During execution 7 Compute p*_(F) that maximizes confidence c_(a)(s₀, p*_(F)). 8 for each a_(h)∈a do 9 Observe the current system state s_(h). 10 if a_(h) is a transition skill then 11 Set free TPs of a according to p*_(F). 12 Compute the most-likely sequence k* of states in θ_(ah). 13 Generate reference trajectory ξ* based on k*. 14 Motion control to track ξ* until the end.

The present invention also includes the use of a robot system, in particular for manipulation of objects, the robot being able to perform a set of skills, for determining a certain sequence comprising at least one transition skill of the set of skills and the at least one core skill of the set of skills, and generating a reference trajectory based in the certain sequence.

Further advantageous embodiments are derived from the following description and the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts first aspect of a method of training a robot system according to an example embodiment of the present invention.

FIGS. 2a to 2d depict different situations of robot systems and an object of interest.

FIG. 3 depicts a robot system in training situation.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 depicts a schematic view of a method 100 of training a robot system 200 according to a first embodiment of the present invention.

The robot system is depicted in a schematic view for example in FIGS. 2a to 2d , and FIG. 3.

The robot system 200 can be used for manipulation of objects. The robot system 200 is configured to perform a set of skills. According to the embodiment, the robot system 200 comprises a gripper and is for example configured to perform a skill “grasp top” as depicted in FIG. 2a which enables the gripper of the robot system to grasp an object 300 at the top of the object 300.

FIG. 2a depicts a situation in which the learned skill “grasp top” results in a poor execution as the object 300 is too far away. Therefore, the situation can be improved by using a transition skill “translate” that pulls the object 300 closer, as shown in FIGS. 2b and 2c , to facilitate the skill “grasp top”. In FIG. 2c , the object 300 has reached a position from which the skill “grasp top” can be executed. A method 100 for training the robot system, in order to enable the robot system to decide whether a transition skill is needed and how the transition skill should be executed, for example where the object should be placed using the transition skill “translate” is described with regard to FIG. 1.

According to an example embodiment of the present invention, the method 100 comprises the following steps:

a step 110 of receiving physical input, in particular from a human trainer, regarding the skill to be learned by the robot, wherein the physical input comprises a set of kinesthetic demonstrations on the robot system; a step 120 of determining for said skill model a set of task parameters, wherein the step of determining the set of task parameters comprises determining for each task parameter of said set of task parameters if a task parameter is an attached task parameter, which is related to an object being part of said kinesthetic demonstration or if a task parameter is a free task parameter, which is not related to a physical object; a step 130 of obtaining data for each task parameter of said set of task parameters from the set of kinesthetic demonstrations, and a step 140 of training said skill model with said set of task parameters and said data obtained for each task parameter.

According to the example embodiments of the present invention, a kinesthetic demonstration involves the movement of the robot system 200, in particular a robot arm 210, in particular an end-effector 220, of the robot system 200. FIG. 3 depicts an exemplary training situation. The end-effector 220 of the robot system 200 is moved by kinesthetic demonstration guided by hand 240 of a human trainer.

According to the example embodiments of the present invention, each skill is learned as a skill model, wherein a skill model is preferably learned as a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model.

The basic feature of learning from demonstration is to fit a prescribed skill model such as GMMs, Gaussian Mixture Models; to a handful of demonstrations. For each skill, the trainer, in particular a human trainer performs several, in particular a number of M_(a) kinesthetic demonstrations on the robot. Each demonstration contains T_(m) data points for a dataset of N=Σ_(m=1) ^(M) T_(m) total observations ξ={ξ_(t)}_(t=1) ^(N) where ξ_(t)∈

^(d). Preferably, the demonstrations are recorded from the perspective of P different coordinate systems TP, which are also referred to as the task parameters. For obtaining data for the task parameters the demonstrations are transformed from global frame to frame p∈TP,

ξ_(t)^((p)) = T_((b_(t)^((p)), A_((t))^((p))))⁻¹(ξ_(t)) = A_(t)^((p)⁻¹)(ξ_(t) − b_(t)^((p))),

where (b_(t) ^((p)), A_(t) ^((p))) is the translation and rotation of frame p with regard to a reference frame, in particular the world frame at time t.

A TP-GMM is described by the parameters

{π_(k), {μ_(k)^((p)), Σ_(k)^((p))}p ∈ TP}_(k = 1)^(K)

where K represents the number of Gaussian components in the mixture model, π_(k) is the prior probability of each component, and μ_(k) ^((p)), Σ_(k) ^((p)) are mean and covariance of the k-th component within frame p.

Once learned, the TP-GMM can be used during execution to reproduce a trajectory for the learned skill. Namely, given the observed frame {(b_(t) ^((p)), A_(t) ^((p))}_(p∈TP), the learned TP-GMM is converted into one single GMM with parameters

{π_(k), {μ_(t, k)^((p)), Σ_(t, k)^((p))}p ∈ TP}_(k = 1)^(K),

by multiplying the affine-transformed Gaussian components across different frames, as follows

${\left( \Sigma_{t,k} \right)^{- 1} = {\sum\limits_{p \in {TP}}\left( \Sigma_{t,k}^{(p)} \right)^{- 1}}},{\mu_{t,k}^{(p)} = {\Sigma_{t,k}{\sum\limits_{p \in {TP}}{\left( \Sigma_{t,k}^{(p)} \right)^{- 1}\mu_{t,k}^{(p)}}}}},$

where parameters of the updated Gaussian at each frame p are computed μ_(t,k) ^((p))=A_(t) ^((p))μ_(k) ^((p))+b_(t) ^((p)) and Σ_(t,k) ^((p))=A_(t) ^((p))Σ_(k) ^((p))A_(t) ^((p)) ^(T) . For more details, reference is made to CALINON Sylvain: “A tutorial on task-parameterized movement learning and retrieval.” Intelligent Service Robotics, 9(1):1-29, 2016.

Hidden semi-Markov Models (HSMMs) extend standard hidden Markov Models (HMMs) by embedding temporal information of the underlying stochastic process. That is, while in HMM the underlying hidden process is assumed to be Markov, i.e., the probability of transitioning to the next state depends only on the current state, in HSMM the state process is assumed semi-Markov. This means that a transition to the next state depends on the current state as well as on the elapsed time since the state was entered.

Exemplary details of applying Hidden semi-Markov Models in combination with Task-Parameterized Gaussian Mixture Models (TP-GMMs), for robot skill encoding to learn spatio-temporal features of the demonstrations are described for example in the following reference: TANWANI, Ajay Kumar, CALINON Sylvain: “Learning Robot Manipulation Tasks with Task-Parameterized Hidden Semi-Markov Model.” IEEE Robotics and Automation Letters, pages 1-8, 2016.

More specifically, a task-parametrized HSMM model consists of the following parameters

θ = {{a_(kh)}_(h = 1)^(K), (μ_(k)^(D), σ_(k)^(D)), {π_(k), {μ_(k)^((p)), Σ_(k)^((p))}_(p ∈ TP)}}_(k = 1)^(K)

where α_(kh) is the transition probality from state k to h; (μ_(k) ^(D), σ_(k) ^(D)) describe the Gaussian distributions for the duration of the state k, i.e., the probability of staying in state k for a certain number of consecutive steps; and

{π_(k), {μ_(k)^((p)), Σ_(k)^((p))}_(p ∈ TP)}_(k = 1)^(K)

is the TP-GMM as described above and for each k, describe the emission probability, i.e., probability of observation, corresponding to state k. The prior π_(k), however, describes in an HSMM only the probability distribution of the initial component at t=1. The probability distribution of the components at subsequent time steps is determined via the underlying Semi-Markov Model. Note that in an HSMM each state corresponds to a Gaussian component in the associated TP-GMM.

Preferably, the structure of the Semi-Markov Model is linear, which means the sequence of states is deterministic and only the duration in each state is probabilistic. This linear structure can be achieved by setting π_(k)=δ_(1k) and α_(kh)=δ_((k+1)h) with δ_(ij)=0 for i≠j and δ_(ij)=1 for i=j. By assuming a linear structure, each skill follows the same segments and is trained in separate model. Preferably, no bifurcations are needed.

Preferably, the aforementioned TP-HSMM formalism is adapted to the Riemannian manifold, for a detailed theory of which reference is made to ZEESTRATEN, Martijn: “Programming by demonstration on Riemannian manifolds.” 2017. PhD thesis.

For each skill, the trainer, in particular a human trainer performs several kinesthetic demonstrations on the robot. Each kinesthetic demonstration comprises a sequence of states consisting of states of an end-effector of the robot system and consisting of states of the object being part of the kinesthetic demonstrations. During demonstration, the end-effector states and objects states are recorded.

Particularly, for skill a∈A, wherein A is a set of manipulation skills, the set of objects involved is given by O_(a) ∈O and the set of demonstrations is given by D_(a)={D₁, . . . D_(Ma)}, where each demonstration is given by D_(m)=[s_(t)]_(t=1) ^(Tm)=[(ξ_(t){p_(t,o), o∈O_(α)})]_(t=1) ^(Tm) where D_(m) is a sequence of states s that consists of the robot end-effector state ξ within the manifold M_(ξ) and object states {p_(o), o∈O_(α)} each within the manifold M_(p). Via a combination of these skills, these objects can be manipulated to reach a desired final state.

According to the present invention, a skill enables the robot system to manipulate an object. In the following it is differentiated between core skills comprising a desired final state of the object and transition skills where the final state of the object can be freely chosen during demonstration.

The set of task parameters of the skill model is essential for the flexibility and generalization of the skill. By this, the characteristics of the demonstration can be learnt from different perspectives. According to the present invention, two different types of task parameters are introduced.

On the one hand, task parameters are usually attached to the objects relevant to the skill and constructed from their poses. These are referred to as attached task parameters. An attached task parameter can be constructed from an object pose p∈M_(p). For instance, for M_(ξ)=M_(p)=

³×S³, the associated task parameter is given by b=p and A=diag(R, I₃) where R is the rotation matrix corresponding to the orientation in p.

On the other hand, for transition skills there are however further relevant task parameters that are not related to a physical object. These are referred to as free task parameters. A free task parameter can not be perceived and should be set explicitly by the user or a planning algorithm. The choice determining a parameter being a free task parameters directly influences the outcome of executing transition skills.

According to an example embodiment of the present invention, the step 120 of determining the set of task parameters comprises choosing the task parameters among the following: task parameters associated with a pose of the object being part of the kinesthetic demonstration, free task parameters, or task parameters associated with a pose, in particular an initial pose, of and end effector of the robot system. In particular, for a skill a, the set of task parameters, denoted by TP_(a) can be chosen among the following: the set of relevant objects O_(a), the set of free task parameters, denoted by F_(a), and the robot arm initial pose, denoted by r. Generally, the set of task parameters can be chosen by attaching frames to all involved objects O_(a) and to the robot arm initial pose indexed by r as well as using the free task parameters F_(a) for transition skills, i.e., TP_(a)=O_(a) ∪F_(a) ∪{r}.

In case that an object produces irrelevant task parameters, which might increase the computation cost and/or decrease the performance of reproduction, the object frame should not be chosen as task parameter. One problem, which might arise with time-varying task parameters like an object pose is that the TP-HSMM only encodes how the task parameter influences the robot arm motion, but not how the robot arm motion affects the objects pose. For example, while executing the skill, which moves the object the trajectory of the robot arm in the frame, attached to the object is only a single constant point, because the object follows every motion of the robot arm while it is grasped. Thus, the robot arm will follow the object during reproduction, i.e., stay where the object is, since the trajectory generation does not know that the robot arm can be moved freely without leaving the single point component in the object frame. In this case, it is better to not to use the object frame as task parameter

According to an example embodiment of the present invention, the step of choosing the task parameters is based on a validation of the reproduction error of the choice. For this, we need a ground truth, which is given as demonstration. Usually, the set of demonstrations is rather small, such that the same set of demonstrations Da is used for training and validation. This yields to the validation:

${V\left( {TP}_{a} \right)} = {\sum\limits_{m = 1}^{M_{a}}\;{\overset{T}{\sum\limits_{t = 1}^{T_{m}}}\;{{\log_{\xi_{t}}\left( \xi_{t} \right)}}}}$

where ξ_(t) is the trajectory retrieved from a skill model for the task parameters TP_(a) from a demonstration, with M_(a) is the number of demonstrations wherein each demonstrations contains Tm data points for a dataset of for a dataset of N=Σ_(m=1) ^(M) T_(m) total observations.

In case that the number of involved objects for a skill is small, the model can be trained for all combinations of task parameters and each choice can be validated using the above described validation. If the number of objects is higher, the trainer might preferably preselect some promising choices of task parameters to reduce the computation time.

According to an example embodiment of the present invention, the method further comprises the step of learning 150 a precondition model of a skill, which refers to a relative relations between the robot system, in particular and end-effector of the robot system, and an object at an initial time. Preferably, the precondition is satisfied when executing a skill to ensure an successful execution. The learned skill model as described above contains information where the robot arm, in particular the end-effector, would start from, but does not incorporate information about the rest of an environment of the robot system, in particular the objects. Such information should include how the objects and the robot arm, in particular the end effector are located with regard to each other when the execution of a specific skill starts. Therefore, according to an embodiment a task parameterized Gaussian, TP-G, is learned for each object to fit its poses from the demonstrations. More specially, the precondition model of a skill is defined by

${\gamma_{1,a}\left( {s,p_{F}} \right)}\overset{\Delta}{=}\left\{ {\left( {\mu_{1,o}^{(p)},\Sigma_{1,o}^{(p)}} \right),{\forall{p \in {{TP}_{a}\backslash\left\{ o \right\}}}}} \right\}_{o \in {O_{a}\bigcup F_{a}}}$

where (μ_(1,o) ^((p)), Σ_(1,o) ^((p))) is the Gaussian distribution of object o's initial pose at time 1 from perspective of object p's initial pose at initial time 1.

Advantageously, the precondition model can be learned purely from the kinesthetic demonstrations performed on the robot system.

According to an example embodiment of the present invention, the method further comprises the step of learning 160 an effect model of skill, which refers to a relative relation between the robot system, in particular, and end-effector of the robot system and an object at a final time. The learned skill model as described above contains information where the robot arm, in particular the end-effector, would stop at, but does not incorporate information about the rest of an environment of the robot system, in particular the objects. Such information should include how the objects and the robot arm, in particular the end effector are located with regard to each other when the execution of a specific skill finishes. Therefore, according to an embodiment a task parameterized Gaussian, TP-G, is learned for each object to fit its poses from the demonstrations. More specifically, the effect model of a skill is defined by

${\gamma_{T,a}\left( {s,p_{F}} \right)}\overset{\Delta}{=}\left\{ {\left( {\mu_{T,o}^{(p)},\Sigma_{T,o}^{(p)}} \right),{\forall{p \in {TP}_{a}}}} \right\}_{o \in O_{a}}$

where (μ_(T,o) ^((p)), Σ_(T,o) ^((p))) is the Gaussian distribution of object o's final pose at time T from the perspective of object p's initial pose at initial time 1.

Advantageously, the skill model can be learned purely from the kinesthetic demonstrations performed on the robot system.

In practice, different task parameters can be chosen for γ_(1,a) and γ_(T,α) to incorporate not only relative but also absolute conditions. Preferably, the skill model and/or the precondition model is computed within the object pose manifold

_(p).

The present invention also includes a robot system 200 configured being trainable via physical input, in particular from a human trainer, regarding the skill to be learned by the robot system 200, wherein the physical input comprises a set of kinesthetic demonstrations on the robot, according a method 100 according to any of the described embodiments.

According to an example embodiment of the present invention, the robot system 200 is configured to track a trajectory with an end-effector of the robot system. Preferably, during demonstration, the trajectory of the end-effector of the robot system can be fetched for example with a control module of the robot system—

According to an example embodiment of the present invention, the robot system 200 is configured to detect objects 300 of interest. For example, the robot system comprises a camera module for detecting the objects 300. Preferably, during demonstration, the task parameters associated with the objects are detect with a camera module of the robot system 200.

The present invention also includes a computer for controlling a robot system 200 according to the embodiments, wherein the computer is configured to execute the method 100 according to the embodiments.

The present invention also includes a computer program comprising computer program code, the computer program code when being executed on a computer enabling the computer to perform the method 100 according to the embodiments.

The present invention also includes a machine-readable storage medium comprising the computer program according the embodiments.

The present invention also includes the use of a robot system 200, in particular for manipulation of objects 300, the robot system 200 being able to perform a set of skills, according to the embodiments for executing a skill sequence comprising a set of skills learned by the robot system according to the method according to any of the embodiments and/or with a computer according to the embodiment and/or with a computer program according to the embodiment.

After determining the optimal choice of free task parameters according to the method described above, a skill sequence is executed as follows. Starting from h=0, the actual system state s_(h) including the poses of all relevant objects and the robot arm are obtained from the state estimation system such as perception and robot state estimator. Then the associated task parameters are constructed from s_(h) according to the optimal choice of task parameters used during the training of the skill model. If a skill is a transition skill, the free task parameters associated with the 1 objects can not be obtained from the state estimation system, instead should be set according to the optimal choice as described above. Thus, given the complete set of task parameters, the GMM components can be computed.

The above process is summarized in the following Algorithm 1. The training process between Line 2 to 5 is done offine for each skill a in the set of skills A. During execution, after observing the initial state s₀, the optimal task parameter p_(F) is computed in Lines 6 and 7. Then, each skill is executed as described in Lines 9 to 14, which makes use of the learned models and the optimization results.

Algorithm 1: Optimize Transition Skills for Manipulation Tasks

Input: Set of skills A; demonstration D_(a) for each a∈A; skill sequence a. 1 for each each a∈A //during training 2 Choose task parameters TPa. 3 Train TP-HSMM model θ_(a) in given TP_(a) and D_(a). 4 Learn the precondition distribution θ1,a in given TP_(1,a) and D_(a). 5 Learn the system state evolution θT,a in given TP_(T,a) and D_(a). 6 Observe the initial system state s₀. //During execution 7 Compute p*_(F) that maximizes confidence c_(a)(s_(o), p*_(F)). 8 for each a_(h) ∈a do 9 Observe the current system state s_(h). 10 if a_(h) is a transition skill then 11 Set free TPs of a according to p*_(F). 12 Compute the most-likely sequence k* of states in θ_(ah). 13 Generate reference trajectory ξ* based on k*. 14 Motion control to track ξ* until the end.

The present invention also includes the use of a robot system 200, in particular for manipulation of objects, the robot system 200 being able to perform a set of skills, for determining a certain sequence comprising at least one transition skill of the set of skills and the at least one core skill of the set of skills, and generating a reference trajectory based on the certain sequence. 

What is claimed is:
 1. A method of training a robot system for manipulation of objects, the robot system being trained to perform a set of skills, wherein each of the skills is learned as a skill model, the skill model being a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model, the method comprising the following steps: receiving physical input from a human trainer regarding a skill to be learned by the robot, wherein the physical input includes a set of kinesthetic demonstrations on the robot system; determining for the skill model a set of task parameters including determining for each of the task parameters of the set of task parameters if the task parameter is an attached task parameter, which is related to an object being part of the kinesthetic demonstration, or if the task parameter is a free task parameter, which is not related to a physical object; obtaining data for each of the task parameters of the set of task parameters from the set of kinesthetic demonstrations; and training the skill model with the set of task parameters and the data obtained for each of the task parameters.
 2. The method according to claim 1, wherein the step of determining the set of task parameters includes choosing task parameters from among the following: (i) task parameters associated with a pose of the object being part of the kinesthetic demonstration, or (ii) free task parameters, or (iii) task parameters associated with an initial pose of an end effector of the robot system.
 3. The method according to claim 2, wherein the step of choosing the task parameters is based on a validation of a reproduction error of the choice.
 4. The method according to claim 1, wherein the skill is learned as a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model.
 5. The method according to claim 1, the method further comprising the following step: learning a precondition model of the skill, which refers to a relative relations between robot system and end-effector of the robot system, and an object at an initial time.
 6. The method according to claim 1, the method further comprising the following step: learning an effect model of the skill which refers to a relative relation between the robot system and end-effector of the robot system, and an object at a final time.
 7. A robot system trainable via physical input from a human trainer, regarding skills to be learned by the robot system, wherein each skill is learned as a skill model, the robot system configured to: receive physical input from a human trainer regarding a skill to be learned by the robot, wherein the physical input includes a set of kinesthetic demonstrations on the robot system; determine for the skill model a set of task parameters including determining for each of the task parameters of the set of task parameters if the task parameter is an attached task parameter, which is related to an object being part of the kinesthetic demonstration, or if the task parameter is a free task parameter, which is not related to a physical object; obtain data for each of the task parameters of the set of task parameters from the set of kinesthetic demonstrations; and train the skill model with the set of task parameters and the data obtained for each of the task parameters
 8. The robot system according to claim 7, wherein the robot system is configured to track a reference trajectory with an end-effector of the robot system.
 9. The robot system according to claim 7, wherein the robot system is configured to detect objects of interest.
 10. A computer for controlling a robot system of manipulation of objects, the robot system being trained to perform a set of skills, wherein each of the skills is learned as a skill model, the skill model being a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model, the computer configured to: receive physical input from a human trainer regarding a skill to be learned by the robot, wherein the physical input includes a set of kinesthetic demonstrations on the robot system; determine for the skill model a set of task parameters including determining for each of the task parameters of the set of task parameters if the task parameter is an attached task parameter, which is related to an object being part of the kinesthetic demonstration, or if the task parameter is a free task parameter, which is not related to a physical object; obtain data for each of the task parameters of the set of task parameters from the set of kinesthetic demonstrations; and train the skill model with the set of task parameters and the data obtained for each of the task parameters.
 11. A non-transitory machine-readable storage medium on which is stored a computer program for training a robot system for manipulation of objects, the robot system being able to perform a set of skills, wherein each of the skills is learned as a skill model, the skill model being a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model, the computer program, when executed by a computer, causing the computer to perform the following steps: receiving physical input from a human trainer regarding a skill to be learned by the robot, wherein the physical input includes a set of kinesthetic demonstrations on the robot system; determining for the skill model a set of task parameters including determining for each of the task parameters of the set of task parameters if the task parameter is an attached task parameter, which is related to an object being part of the kinesthetic demonstration, or if the task parameter is a free task parameter, which is not related to a physical object; obtaining data for each of the task parameters of the set of task parameters from the set of kinesthetic demonstrations; and training the skill model with the set of task parameters and the data obtained for each of the task parameters.
 12. A method of using a robot system for manipulation of objects, the method comprising the following steps: providing the robot system; training the robot system for manipulation of objects, the robot system being trained to perform a set of skills, wherein each of the skills is learned as a skill model, the skill model being a TP-HSMM, Task Parameterized Hidden semi-Markov Model, combined with a TP-GMM, Task Parameterized Gaussian Mixture Model, the robot system being trained to perform each of the set of skills by: receiving physical input from a human trainer regarding the skill to be learned by the robot, wherein the physical input includes a set of kinesthetic demonstrations on the robot system; determining for the skill model a set of task parameters including determining for each of the task parameters of the set of task parameters if the task parameter is an attached task parameter, which is related to an object being part of the kinesthetic demonstration, or if the task parameter is a free task parameter, which is not related to a physical object; obtaining data for each of the task parameters of the set of task parameters from the set of kinesthetic demonstrations; and training the skill model with the set of task parameters and the data obtained for each of the task parameters; and preforming, by the robot system, a skill sequence including the set of skills learned by the robot system. 